COMPARING COMPUTABILITY IN TWO TOPOLOGIES

Computable analysis provides ways of representing points in a topological space, and therefore defining notion computable the space. In this article, we investigate when two topologies on same space induce different sets points. We first study purely version problem, which is to understand are not -homeomorphic. obtain characterization leading an effective version, prove that satisfying condition Along way, propose Baire category theorem captures construction technique, enables one build properties co-meager with respect topology, another topology. Finally, generalize result three give application certain do have type, means they homeomorphic copy semicomputable but computable.